Article Volume 12, Issue 1, 2022, 339 - 350 https://doi.org/10.33263/BRIAC121.339350

Effect of the Temperature and Solvents on the Solvolysis of in Aqueous-Organic Solutions: Volumetric and Viscometric Study

Sudhansu Sekhar Pattnaik 1 , Binita Nanda 2 , Biswajit Dalai 1 , Braja B. Nanda 3, *

1 Department of Physics, GIET University, Gunupur, Odisha, India; [email protected] (S.S.P.); 2 Department of Chemistry, ITER, Sikshya ‘O’ Anusandhan (Deemed to be University), Bhubaneswar-751030, India; [email protected] (B.N.); 3 P.G. Department of Chemistry, Vikram Deb Autonomous College, Jeypore-764001, Odisha, India; [email protected] (B.B.N.); * Correspondence: [email protected]; Scopus Author ID 8431581400 Received: 23.02.2021; Revised: 2.04.2021; Accepted: 7.04.2021; Published: 20.04.2021

Abstract: Volumetric and viscometric properties of solutions containing barium bromide in an aqueous solution of ethylene glycol and 1,4-dioxane have been discussed at different temperatures such as 298.15K 303.15K, 308.15K, and 313.15K. The Masson’s equation was used to determine the apparent 0 0 molar volume, 푉휙, standard partial molar volume, 푉휙 , molar expansibilities,퐸휙 by taking the density data. The values of viscosity and density were used in the Jones-Dole equation to find the viscosity B coefficients, which were used to estimate the -solvent interactions. The values of Hepler’s constant 2 0 2 (휕 푉휙 / 휕T )p and the viscosity B-coefficients have been used to deduce the solvent structure-promoting or structure breaking tendency of the in the studied mixtures. In the current study, the positive values of Hepler’s constant and the negative values of dB/dT show that barium bromide in the considered solvents mainly behaves as a structure promoter.

Keywords: Apparent molar volume; Hepler’s constant; barium bromide; Jones–Dole equation. © 2021 by the authors. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

1. Introduction

Partial molar volume and viscosity data provide valuable evidence about different types of forces of attractions present in the solutions [1-5]. The volumetric and viscometric studies of solutions help us illustrate solutes' organization and properties in mixed solvents [6-10]. Recently, many researchers have studied the solution properties of the different salts in mixed solutions [11-16]. Frank and Evan [17] have interpreted the thermodynamic properties of the aqueous-organic solutions in terms of water particles' organization about the non-polar solute. 1, 4-Dioxane is a heterocyclic colorless organic liquid having a faint sweet smell like to diether. It is used as a (i) versatile aprotic solvent for cellulose esters, inks, and adhesives, (ii) as a stabilizer for transporting chlorinated hydrocarbons in aluminum vessels. Due to its lower toxicity and higher boiling point, it substituted Tetrahydrofuran in some reactions and was used as an internal standard for NMR spectroscopy of deuterium oxide. It serves as a chelating diether ligand and can solvate many inorganic compounds due to the presence of two oxygen atoms in it. Similarly, ethylene glycol is used in many commercial and industrial applications, including antifreeze and coolant. The salt, barium bromide, BaBr2 have many applications in

https://biointerfaceresearch.com/ 339 https://doi.org/10.33263/BRIAC121.339350 the field of chemical reactions. It is used as a precursor to chemicals used in photography and used to purify in the fractional process. This paper is dealt with the study of the ion-solvent, ion-ion, and solvent-solvent interactions of the barium bromide with the aqueous solutions of dioxane and ethylene glycol, as both the solute and the solvents are used for industrial processes. Therefore, the volumetric and viscometric properties of BaBr2 in aqueous-organic solvents such as 1, 4-dioxane, and ethylene glycol, have been studied to evaluate the ion-solvent and ion-ion interactions existing among the solutes and solvents.

2. Materials and Methods

2.1. Chemicals.

Anhydrous barium bromide, ethylene glycol, and 1,4-dioxane used were taken from Sigma Aldrich, Germany, with more than 99% purity and then refined by standard methods [18]. The triply distilled water was used to prepare the solutions of 10, 20, and 30(v/v) % of each of ethylene glycol and dioxane solutions, which served as solvents. Barium bromide was further desiccated over anhydrous CaCl2 before use [19]. The sample specification is given in Table 1. Table 1. Specification of Chemicals. Chemicals Source Mass fraction Purification CAS No Mol.Mass/ Structure puritya method g mol-1 Barium bromide Sigma- 0.99 Used as 10553-31-8 297.14 BaBr2 Aldrich obtained Ethylene Glycol Sigma- >0.998 By standard 107-21-1 62.07 Aldrich methods[18]

1,4-Dioxane Sigma- >0.99 By standard 123-91-1 88.11 Aldrich methods[18] aAs declared by the supplier

2.2. Apparatus and procedure.

The masses of the solute and solvents were measured by electronic balance (KERN, model ABJ-220-4NM, made in Germany) with a precision of ± 0.01mg. A double arm pycnometer was taken to determine the density (ρ) of the prepared solutions at T=(298.15- 313.15) K, which was calibrated with deionized triply distilled water with 997.017 kg/m3 as its density at temperature 298.15 K. The measurement of viscosity of the solutions was done with the help of Ostwald viscometer with appropriately long reflux period greater than 200 seconds to avoid the corrections in kinetic energy. The average of three readings from the Ostwald viscometer was taken into consideration. The density bottle and viscometer were calibrated [20-21] using distilled water. All the measurements are carried out by clamping pyknometer and viscometer in a water bath maintained at constant temperatures ±0.01 K. The uncertainty in viscosity and density measurements were within ±0.003 mPa and 1 ×10-5 g cm-3 respectively. The water's viscosity was taken to be 0.7194×10-3 kg m-1 s-1 (at 303.15K) [22]. The molar concentrations of the solutions were converted to molality using the standard formula using the density values.

https://biointerfaceresearch.com/ 340 https://doi.org/10.33263/BRIAC121.339350 3. Results and Discussion

3.1. Viscometric study:

The properties of electrolytic solutions in aqueous media are highly particular to the individual of the respective electrolyte, so it is difficult to generalize these properties. Another parameter to find the ion solvent interactions is the determination of transport property in terms of viscosity. The formula: η/ηo= (t × ρ)/ (t0 × ρ0) was used to calculate the relative viscosity of the solutions, where η is the absolute viscosity, t is the time of flow and ρ is the density of solution respectively, while η0, t0, and ρ0 are the same measure for the solvent respectively. The densities of solutions are tabulated in Table 2. The dependence of viscosities of BaBr2 solutions in aqueous dioxane and ethylene glycol with the molality can be expressed by the Jones-Dole equation [23] as given below:

휂푟= η /ηo = 1+A √푚퐴+ B푚퐴 (1)

Where 휂푟 is the relative viscosity of the studied solutions, η and ηo are the viscosities of solutions and solvent, respectively. The constant A represents the interionic forces [24-25], and known as the Falkenhagen coefficient, the coefficient B is associated with the solute-solvent interactions and is understood as a degree of the structure-promoting or structure breaking nature of the ions in the said solutions [26]. The parameters A and B can be found by arranging equation 1 as follows:

(η/ηo ‒1) / √푚퐴 = sp/√푚퐴 = A + B √푚퐴 (2)

(η/ηo ‒1) is known as specific viscosity and represented as sp. The values of (η/ηo ‒1)/ √푚퐴 and the parameters A and B coefficients of the above equation are tabulated in Tables 3 and 4, respectively. The variation of (η/ηo ‒1)/ √푚퐴 with molality ‘√푚퐴 ’ indicates the decrease of viscosity with the increase in temperature and viscosity increase with an increase of dioxane/ethylene glycol content in the solutions. The variation of viscosity with the molal concentration of solutions at 298.15 K is given in Figure 1.

(a) (b) 1/2 1/2 Figure 1. The plot (휂⁄휂0 − 1)/mA vs. mA of BaBr2 in (a) DO -Water and (b) EG -Water respectively at 298.15K.

The intermolecular force of attraction increases with an increase in the mass fraction of BaBr2 in the solution; as a result, the viscosity of the solution increases. The positive values of

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coefficient A at all temperatures for BaBr2 prove the existence of substantial ion-ion interactions. The viscosity B coefficient of the Jones-Dole equation indicates the presence of ion-solvent interaction [22]. For all the solutions, the values of viscosity B coefficients may be positive or negative. If the solute attracts the water/solvent molecules, then its B coefficient value will be positive; otherwise, it will be negative. In the present study, the positive values of viscosity B coefficient for BaBr2 in both dioxane-water and ethylene glycol-water media (Table 4) confirms the existence of ion-solvent interactions. The negative values of thermal coefficient (dB/dT) [25] indicate that there are strong ion-solvent interactions and the said solute is a structure promoter in the studied media. These data agree with the result obtained from the Hepler equation discussed in volumetric properties [27].

Table 2. Density, ρ, and apparent molar volume, 푉휙 of Barium bromide in ethylene glycol-water and 1,4- dioxane-water respectively at T= (298.15 – 313.15)K. −ퟑ ퟓ ퟑ −ퟏ 풎푨/ ρ / 풌퐠 퐦 푽흓 × ퟏퟎ / 퐦 퐦퐨퐥 풎풐풍 풌품−ퟏ 298.15K 303.15K 308.15K 313.15K 298.15K 303.15K 308.15K 313.15K 10:90 (v/v) 1,4-Dioxane-Water 0.0000 1013.3 1010.0 1007.0 1003.9 0.0010 1013.5 1010.2 1007.2 1004.1 5.1502 4.9399 4.5451 4.1607 0.0025 1013.9 1010.6 1007.6 1004.5 5.5678 5.3140 5.1351 4.8634 0.0049 1014.4 1011.2 1008.2 1005.1 6.1043 5.7958 5.5075 5.2943 0.0074 1015.0 1011.7 1008.7 1005.6 6.4401 6.2476 5.9790 5.6381 0.0099 1015.6 1012.3 1009.3 1006.2 6.6259 6.4674 6.2703 6.1036 0.0247 1019.0 1015.8 1012.8 1009.7 6.8233 6.6435 6.4444 6.2758 0.0495 1024.7 1021.5 1018.6 1015.5 6.8233 6.6298 6.4279 6.2793 0.0744 1030.4 1027.2 1024.4 1021.3 6.8233 6.6428 6.4505 6.2828 0.0994 1036.1 1033.0 1030.1 1027.0 6.8233 6.6503 6.4535 6.2868 20:80 (v/v) 1,4-Dioxane-Water 0.000 1027.5 1024.2 1021.1 1018.2 0.0010 1027.7 1024.4 1021.3 1018.4 5.0887 4.9308 4.8321 4.7113 0.0024 1028.1 1024.8 1021.7 1018.8 5.5433 5.3440 5.2375 5.0741 0.0049 1028.6 1025.3 1022.2 1019.3 6.0307 5.7412 5.5583 5.3740 0.0073 1029.2 1025.9 1022.8 1019.9 6.3362 6.1568 5.8777 5.7248 0.0097 1029.8 1026.5 1023.4 1020.5 6.5983 6.4128 6.2053 5.9554 0.0244 1033.1 1029.8 1026.8 1023.9 7.1183 6.9642 6.8318 6.6776 0.0488 1038.7 1035.5 1032.4 1029.5 7.1540 7.0025 6.8701 6.7172 0.0734 1044.3 1041.1 1038.1 1035.2 7.1717 7.0325 6.8960 6.7786 0.0980 1049.8 1046.6 1043.7 1040.8 7.2156 7.0743 6.9288 6.7949 30:70 (v/v) 1,4-Dioxane-Water 0.0000 1040.6 1037.6 1034.5 1031.1 0.0010 1040.8 1037.8 1034.7 1031.3 5.4409 5.1258 4.9442 4.7757 0.0024 1041.2 1038.2 1035.1 1031.7 5.9635 5.7599 5.5382 5.3099 0.0048 1041.7 1038.7 1035.7 1032.3 6.7727 6.5976 6.2695 6.0711 0.0072 1042.3 1039.3 1036.2 1032.8 7.1435 6.9335 6.7532 6.6015 0.0096 1042.8 1039.8 1036.7 1033.3 7.3617 7.2174 7.0618 6.8803 0.0241 1046.1 1043.1 1040.0 1036.6 7.5650 7.4405 7.3320 7.1682 0.0482 1051.5 1048.5 1045.5 1042.1 7.6052 7.4768 7.3510 7.2213 0.0725 1056.9 1054.0 1051.0 1047.6 7.6259 7.5030 7.3692 7.2395 0.0968 1062.4 1059.5 1056.5 1053.1 7.6052 7.4731 7.3718 7.2589 10:90 (v/v) Ethylene glycol-Water 0.0000 1029.3 1026.1 1022.9 1020.1 0.0010 1029.5 1026.3 1023.1 1020.4 4.7909 4.6093 4.4940 4.2312 0.0024 1029.9 1026.7 1023.5 1020.7 5.5514 5.3268 5.2447 5.1021 0.0049 1030.5 1027.3 1024.1 1021.3 5.9678 5.7101 5.5781 5.4309 0.0073 1031.0 1027.9 1024.7 1021.9 6.2968 6.0923 6.0090 5.9084 0.0097 1031.6 1028.4 1025.2 1022.4 6.5556 6.3522 6.2673 6.1455 0.0243 1035.0 1031.8 1028.7 1025.9 6.7251 6.5291 6.4054 6.2817 0.0487 1040.7 1037.5 1034.4 1031.6 6.7496 6.5736 6.4268 6.3243 0.0732 1046.4 1043.3 1040.2 1037.4 6.7578 6.5811 6.4219 6.3110 0.0978 1052.1 1049.0 1045.9 1043.2 6.7578 6.5946 6.4304 6.3118 20:80 (v/v) Ethylene glycol-Water 0.0000 1047.9 1044.8 1041.5 1038.3 0.0010 1048.1 1045.0 1041.7 1038.5 5.2452 4.7600 4.6564 4.4079

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−ퟑ ퟓ ퟑ −ퟏ 풎푨/ ρ / 풌퐠 퐦 푽흓 × ퟏퟎ / 퐦 퐦퐨퐥 풎풐풍 풌품−ퟏ 298.15K 303.15K 308.15K 313.15K 298.15K 303.15K 308.15K 313.15K 0.0024 1048.5 1045.4 1042.1 1038.9 5.7054 5.1947 5.3334 5.2514 0.0048 1049.1 1046.0 1042.7 1039.5 6.0659 5.9152 5.7675 5.5599 0.0072 1049.6 1046.5 1043.2 1040.0 6.4556 6.2779 6.1835 6.0356 0.0095 1050.2 1047.1 1043.8 1040.6 6.6821 6.5313 6.3868 6.2443 0.0239 1053.5 1050.5 1047.2 1044.0 6.8675 6.7016 6.5560 6.4257 0.0479 1059.1 1056.1 1052.8 1049.7 6.9143 6.7278 6.6085 6.4789 0.0720 1064.7 1061.8 1058.5 1055.4 6.9210 6.7453 6.6276 6.4892 0.0961 1070.3 1067.4 1064.2 1061.1 6.9363 6.7617 6.6295 6.4892 30:70 (v/v) Ethylene glycol-Water 0.0000 1081.6 1064.0 1056.0 1047.9 0.0009 1081.8 1064.2 1056.2 1048.1 5.3812 4.9981 4.8071 4.6325 0.0023 1082.2 1064.6 1056.6 1048.5 5.8372 5.5463 5.4131 5.4023 0.0046 1082.7 1065.1 1057.1 1049.0 6.2212 6.0071 5.9089 5.8170 0.0069 1083.3 1065.7 1057.7 1049.6 6.6128 6.3893 6.2976 6.1661 0.0093 1083.8 1066.2 1058.2 1050.1 6.8095 6.6536 6.6242 6.3898 0.0232 1087.1 1069.5 1061.5 1053.4 7.1047 6.8731 6.7934 6.5610 0.0464 1092.6 1075.0 1067.0 1058.9 7.1582 6.9222 6.8305 6.6052 0.0697 1098.1 1080.5 1072.5 1064.5 7.1716 6.9288 6.8644 6.6323 0.0932 1103.6 1086.0 1077.9 1070.0 7.1773 6.9353 6.8819 6.6478

1/2 Table 3. (η/η0-1)/m of BaBr2 in 10-30 % (v/v) ethylene glycol-water and 1,4-dioxane-water respectively at T = (298.15-313.15) K and at atmospheric pressure. 풎푨/ 298.15K 303.15K 308.15K 313.15K 풎푨 298.15K 303.15K 308.15K 313.15K 푚표푙 푘푔−1 10:90 (v/v) 1,4-Dioxane-Water 푚표푙 푘푔−1 10:90 (v/v) Ethylene glycol-Water 0.0010 0.057 0.054 0.054 0.052 0.0010 0.061 0.059 0.055 0.052 0.0025 0.070 0.068 0.066 0.064 0.0024 0.075 0.072 0.067 0.063 0.0049 0.085 0.083 0.081 0.079 0.0049 0.092 0.088 0.082 0.077 0.0074 0.096 0.095 0.092 0.090 0.0073 0.105 0.101 0.093 0.087 0.0099 0.107 0.105 0.102 0.099 0.0097 0.116 0.111 0.102 0.097 0.0247 0.150 0.147 0.142 0.138 0.0243 0.163 0.156 0.143 0.134 0.0495 0.199 0.195 0.188 0.183 0.0487 0.216 0.206 0.189 0.177 0.0744 0.236 0.231 0.223 0.217 0.0732 0.256 0.246 0.225 0.211 0.0994 0.267 0.261 0.252 0.245 0.0978 0.290 0.278 0.254 0.238 20:80 (v/v) 1,4-Dioxane-Water 20:80 (v/v) Ethylene glycol-Water 0.0010 0.058 0.058 0.058 0.058 0.0010 0.065 0.062 0.058 0.055 0.0024 0.073 0.071 0.071 0.070 0.0024 0.082 0.078 0.072 0.068 0.0049 0.090 0.087 0.086 0.084 0.0048 0.101 0.097 0.087 0.083 0.0073 0.103 0.099 0.097 0.094 0.0072 0.117 0.111 0.105 0.093 0.0097 0.113 0.110 0.107 0.104 0.0095 0.129 0.122 0.119 0.103 0.0244 0.160 0.155 0.151 0.146 0.0239 0.183 0.173 0.166 0.144 0.0488 0.212 0.205 0.200 0.194 0.0479 0.244 0.230 0.212 0.191 0.0734 0.252 0.244 0.238 0.230 0.0720 0.290 0.274 0.250 0.227 0.0980 0.286 0.277 0.270 0.261 0.0961 0.330 0.311 0.285 0.256 30:70 (v/v) 1,4-Dioxane-Water 30:70 (v/v) Ethylene glycol-Water 0.0010 0.061 0.061 0.058 0.057 0.0009 0.072 0.069 0.066 0.062 0.0024 0.078 0.075 0.075 0.074 0.0023 0.089 0.085 0.083 0.079 0.0048 0.097 0.094 0.092 0.090 0.0046 0.112 0.106 0.103 0.099 0.0072 0.111 0.107 0.106 0.103 0.0069 0.128 0.121 0.119 0.113 0.0096 0.123 0.119 0.117 0.114 0.0093 0.142 0.135 0.131 0.124 0.0241 0.175 0.169 0.166 0.161 0.0232 0.202 0.191 0.186 0.175 0.0482 0.233 0.224 0.220 0.213 0.0464 0.269 0.254 0.248 0.234 0.0725 0.277 0.267 0.262 0.254 0.0697 0.321 0.303 0.295 0.278 0.0968 0.315 0.303 0.298 0.288 0.0932 0.364 0.344 0.328 0.315

Table 4. The values of A and viscosity B-coefficient of BaBr2 in 10-30 % (v/v) ethylene glycol-water and 1,4- dioxane-water respectively at T = (298.15-313.15) K and at atmospheric pressure. T/K Parameters 10:90 DO- 20:80 30:70 10:90 20:80 30:70 Water DO-Water DO-Water EG-Water EG-Water EG-Water

퐴 0.033±0.000 0.033±0.000 0.034±0.000 0.036±0.0003 0.036±0.000 0.039±0.0004 퐵 0.743±0.001 0.809±0.002 0.906±0.002 0.813±0.0017 0.949±0.002 1.066±0.0021

σ 0.0004 0.0005 0.0006 0.0005 0.0005 0.0006 298.15

퐴 0.032±0.000 0.033±0.000 0.034±0.000 0.034±0.0002 0.035±0.000 0.038±0.0003 퐵 0.730±0.002 0.778±0.001 0.867±0.002 0.778±0.0012 0.891±0.002 1.004±0.0020

σ 0.0005 0.0004 0.0005 0.0004 0.0006 0.0006 303.15

8. 15 30 퐴 0.032±0.000 0.033±0.000 0.033±0.000 0.032±0.0001 0.035±0.002 0.038±0.0014 https://biointerfaceresearch.com/ 343 https://doi.org/10.33263/BRIAC121.339350

T/K Parameters 10:90 DO- 20:80 30:70 10:90 20:80 30:70 Water DO-Water DO-Water EG-Water EG-Water EG-Water 퐵 0.700±0.001 0.755±0.002 0.851±0.003 0.710±0.0006 0.811±0.012 0.964±0.0082 σ 0.0002 0.0005 0.0007 0.0002 0.0035 0.0023

퐴 0.031±0.000 0.033±0.001 0.033±0.000 0.031±0.0001 0.033±0.000 0.035±0.0004 퐵 0.681±0.001 0.726±0.003 0.820±0.003 0.663±0.0008 0.723±0.001 0.919±0.0023

313.15 σ 0.0004 0.0009 0.0007 0.0002 0.0002 0.0007

3.2. Volumetric study.

Apparent molar volume is the change in the volume of the solute molecules due to the interaction with the solvents in a solution. From the experimentally obtained density data, we

can calculate the apparent molar volume, 푉휙 of the solute using the equation as follows [28]: 0 푀2 (휌 − 휌) 푉휙= + 0 (3) 휌 푚퐴 휌 휌 -3 -3 Where ρ0 / kg m is the density of the pure solvent, ρ / kg m is the solution's density, mA/mol -1 -1 kg is the molality, and M2 / kg mol is the molecular weight of solute. The 푉휙 values (Table 2) have been found to be positive and increase with an increase in solute concentration and

decrease with rising in temperature. 푉휙 values of BaBr2 in aqueous solvents increase in the following order: ethylene glycol-water<1,4-dioxane-water. The Masson-type equation can be 0 3 −1 employed to calculate the partial molar volume,푉휙 /m mol , [29] as given below:

0 푒푥 푉휙= 푉휙 + 푆푣 √푚퐴 (4)

0 푒푥 The values of 푉휙 and the coefficients 푆푣 of equation (4) are obtained by plotting the 0 graph 푉휙 푣푠 √푚퐴 at four different temperatures are given in Table 5. The plot of 푉휙 vs. mA are presented in Figure 2.

(a) (b) (c)

(d) (e) (f)

Figure 2. Plot of 푉휙 vs. 푚퐴 of BaBr2 in (a) 10% (v/v) 1,4-dioxane –water, (b) 20% (v/v) 1,4-dioxane –water, (c) 30% (v/v) 1,4-dioxane –water, (d) 10% (v/v) ethylene glycol –water, (e) 20% (v/v) ethylene glycol –water,(f) 30% (v/v) ethylene glycol-water solutions at T=( 298.15 – 313.15) K.

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2 (푌 −푌 ) The standard deviation was calculated as per the formula, σ = √[ 푐푎푙 푒푥푝 ]. It has 푓

0 been found that 푉휙 for the investigated BaBr2 solutions in the said solvents decrease with the 0 concentration of dioxane and glycol. All the 푉휙 values are found to be large and positive for all the solutions(Table 5). It is known the properties like density, viscosity, etc., are influenced by the presence of –OH group or oxygen atom in a molecule. The presence of such groups increases the hydrophilicity and electrostriction between water and solute particles. The 0 decreasing trend of 푉휙 values in dioxane-water and glycol-water indicate the ion-solvent interactions. In very dilute solutions, the ions are encircled by the solvent molecules so they 0 are present far away from each other. So 푉휙 is affected by ion-solvent interactions only. With an increase in temperature, some of the solvent molecules are freed from the loose solvation 0 layers; as a result, the values of 푉휙 decrease with an increase in temperature. With the addition of organic solvents, there will be the formation of strong solvation layers around the ions 0 0 resulting increase in 푉휙 values. In this case, the values of 푉휙 of BaBr2 in DO-water/EG-water is in the order: In Water <10:90 DO-Water <20:80 DO-Water <30:70 DO-Water In Water<10:90 EG-Water <20:80EG-Water <30:70EG-Water

0 Table 5. Partial molar volume, 푉휙 , experimental slope, 푆푣, and their standard deviations for BaBr2 in pure water , 1,4-dioxane-water, and ethylene glycol-water at T=(298.15 – 313.15)K and at and 0.1 MPa Pressure. Parameters In Water 10:90 DO- 20:80 30:70 10:90 20:80 30:70

Water DO-Water DO-Water EG-Water EG-Water EG-Water

푉0× 105 / 푚3 푚표푙−1

휙 5.312 ± 0.16 5.67±0.25 5.818±0.25 6.145±0.33 5.498±0.28 5.720±0.23 5.838±0.24 5 9/2 −3/2 푆푣× 10 / 푚 푚표푙 3.651± 0.78 4.667±1.45 6.637±1.47 6.044±1.93 5.154±1.64 4.924±1.36 5.492±1.40

σ × 105 / 3 −1 0.301 0.422 0.423 0.553 0.474 0.390 0.394 5 298.1 푚 푚표푙 0 5 3 −1

푉휙 × 10 / 푚 푚표푙 5.221 ± 0.12 5.437±0.26 5.602±0.25 5.908±0.35 5.272±0.28 5.369±0.30 5.567±0.27 5 9/2 −3/2 푆푣× 10 / 푚 푚표푙 4.102 ±0.59 4.903±1.50 6.899±1.45 6.493±2.06 5.347±1.61 5.689±1.76 5.664±1.60 σ × 105 / 3 −1

303.15 푚 푚표푙 0.222 0.436 0.420 0.591 0.464 0.503 0.450 0 5 3 −1

푉휙 × 10 / 푚 푚표푙 5.103 ± 0.12 5.147±0.28 5.133±0.24 5.671±0.36 5.188±0.29 5.318±0.28 5.435±0.29 5 9/2 −3/2 푆푣× 10 / 푚 푚표푙 4.230 ± 0.57 5.281±1.61 6.980±1.36 6.954±2.07 5.088±1.65 5.366±1.64 5.945±1.72 σ × 105 / 3 −1

308.15 푚 푚표푙 0.2 0.469 0.392 0.595 0.476 0.469 0.485 0 5 3 −1

푉휙 × 10 / 푚 푚표푙 5.001 ± 0.12 4.837±0.31 4.954±0.22 5.465±0.36 5.013±0.31 5.143±0.30 5.336±0.28 5 9/2 −3/2 푆푣× 10 / 푚 푚표푙 5.32 ± 0.57 5.869±1.76 7.121±1.28 7.254±2.07 5.351±1.79 5.528±1.72 5.411±1.66 σ × 105 / 3 −1 0.235 0.512 0.371 0.595 0.515 0.492 0.469

313.15 푚 푚표푙

3.3. The temperature dependency of partial molar volume.

0 The temperature dependency of 푉휙 values of BaBr2 in aqueous solutions of dioxane and ethylene glycol can be evaluated from the following polynomial equation [30].

0 2 푉휙 =a0+a1T+a2T (5)

The value of coefficient a0, a1, and a2 in equation(5) has been evaluated from the least- 0 squares fitting of the 푉휙 values at T=(398.15-313.15)K and are presented in Table 6. The 0 partial molar isobaric expansivity, 퐸훷, is the factor that gives the change of partial molar 0 volume with temperature can be found by different 푉휙 concerning T at constant pressure is given below as: 0 0 퐸훷=(∂푉휙 /∂T)p=a1+2a2T (6)

https://biointerfaceresearch.com/ 345 https://doi.org/10.33263/BRIAC121.339350 The extent of solute-solvent interactions and solvation nature of the solute can be found 0 from the values of 퐸훷 [31]. On the rising temperature, certain water molecules may be freed 0 from the solvation sheet and hence increasing the volume of solution and 퐸훷 values become 0 negative. It has been observed that the 퐸훷 values rise with rising temperatures that indicate the absence of caging effect.

Table 6. Values of various coefficients (Equation (5)), of BaBr2 in 10-30 % (v/v) ethylene glycol-water and 1,4- dioxane-water respectively at T = (298.15-313.15) K and at 0.1 MPa pressure. ퟓ ퟓ ퟗ 5 Solvents a0 × ퟏퟎ / a1 × ퟏퟎ / a2 × ퟏퟎ / σ × 10 / 풎ퟑ 풎풐풍−ퟏ m3 mol-1 k-1 m3 mol-1 K-2 풎ퟑ 풎풐풍−ퟏ 10:90 DO-W 40.9±16.8 -0.20±0.11 2.764±1.80 0.009 20:80 DO-W 44.7±24.1 -0.22±0.16 3.100±2.58 0.013 30:70 DO-W 57.3±30.1 -0.30±0.20 4.361±3.23 0.016 10:90 EG-W 14.3±14.4 -0.03±0.09 -0.164±1.54 0.008 20:80 EG-W 50.3±23.1 -0.26±0.15 3.610±2.48 0.012 30:70 EG-W 49.1±12.8 -0.24±0.08 3.153±1.37 0.007

0 Hepler’s equation[27] can be calculated by differentiating 퐸훷 w.r.t temperature T and given as follows: 0 2 0 2 (∂퐸훷/∂T)p=(∂ 푉휙 /∂T )p=2a2 (7)

For deciding whether the solute is a structure promoter or structure breaker, the sign of 2 0 2 2 0 (∂ 푉휙 /∂T )p value is a better criterion [25]. The positive or small negative values of (∂ 푉휙 2 /∂T )p shows that the solute is a structure promoter, and the negative value indicates the reverse. 2 0 2 In the present study, it has been found that the values of (∂ 푉휙 /∂T )p are all positive (Table 7), which indicates that BaBr2 mostly acts as a structure promoter in the studied solutions over the entire ranges of temperature studied.

Table 7. Values of Limiting partial molar expansibilities (Equation 6)) and Hepler’s constant (Equation (7)) of

BaBr2 in aqueous solutions of 1,4-dioxane(DO) and ethylene glycol (EG) at T=(298.15 to 313.15) K. 0 7 3 -1 -1 0 Solvents 푑퐸휙,푣 퐸휙,푣 × 10 /m mol K 109 ( )/ 푑푇 298.15 K 303.15 K 308.15 K 313.15 K (m3 mol-1) 10:90 DO-W -3.62 -3.34 -3.07 -2.79 5.528 20:80 DO-W -3.84 -3.53 -3.22 -2.91 6.201 30:70 DO-W -4.27 -3.83 -3.39 -2.96 8.722 10:90 EG-W -3.54 -3.56 -3.58 -3.59 -0.328 20:80 EG-W -4.26 -3.90 -3.54 -3.18 7.219 30:70 EG-W -5.02 -4.71 -4.39 -4.08 6.305

The isobaric thermal expansion coefficient (α) can be calculated from equation 8 and presented in Table 8:

0 0 α =( 퐸훷/푉ϕ ) (8)

The structure–making or structure-breaking nature of a solute in an aqueous mixed solvent can best be understood by an equation given by L. G. Hepler[27].

(휕퐶0⁄휕푃) = - T(휕2푉0⁄휕푇2) (9) 푝 휙 푝

From this expression, it can be calculated that structure–making solutes have a negative 0 value of (휕퐶푝 ⁄휕푃), whereas the structure-breaking solutes have positive values. The values

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0 of (휕퐶푝 ⁄휕푃) are found to be negative ( Table 8) for both solvents. This indicates that BaBr2 is a structure promoting solutes in the studied solutions.

3.4. Transport behavior.

0 The standard partial molar volumes of transfer, ∆푡푉ϕ and B-coefficient of transfer

∆푡퐵 of BaBr2 from water to an aqueous solution of DO/EG were computed using the following equations: 0 0 0 ∆푡푉ϕ =푉ϕ (BaBr2 in aqueous DO or EG)‒ 푉ϕ (in water) (10)

∆푡퐵 = B(BaBr2 in aqueous DO or EG) ‒ B (in water) (11)

0 By definition, the values of ∆푡푉ϕ deliver ideas about the ion-solvent interactions. The 0 values of ∆푡푉ϕ and ∆푡퐵 obtained from equations (10 and 11) are listed in Table 9. The plot of 0 ∆푡푉ϕ and ∆푡퐵 with percentage composition of DO and EG are given in Figure 3.The positive 0 values of ∆푡푉ϕ and ∆푡퐵, can be interpreted by Krishnan and Friedman’s cosphere overlap model [32]. The existence of ion-solvent interfaces is due to positive values of transfer volume. 0 The increased value of ∆푡푉ϕ and ∆푡퐵 with an increase of the percentage of DO/EG in solution 0 represents the presence of attraction of DO/EG with BaBr2. The values of ∆푡푉ϕ also, increases with the rise of temperatures are due to the lessening of electrostriction of BaBr2 at higher values of temperature.

0 Table 8. The values of 훼 and (휕퐶푝 ⁄휕푃) of BaBr2 in ethylene glycol- -water and 1,4-dioxane- water at T=(298.15- 313.15) K. 3 ퟎ 9 3 -1 -1 휶ퟏ × 10 / K (흏푪풑⁄흏푷) ×10 /m mol K Solvents 298.15K 303.15K 308.15K 313.15K 298.15K 303.15K 308.15K 313.15K 10:90 -6.91 -6.60 -6.29 -5.93 -0.165 -0.168 -0.170 -0.173 DO-W 20:80 -6.40 -6.07 -5.67 0.13 -0.185 -0.188 -0.191 -0.194 DO-W 30:70 -6.23 -5.75 -5.22 0.16 -0.260 -0.264 -0.269 -0.273 DO-W 10:90 -6.48 -6.73 -6.95 -0.01 0.010 0.010 0.010 0.010 EG-W 20:80 -6.90 -6.49 -5.99 0.14 -0.215 -0.219 -0.222 -0.226 EG-W 30:70 -8.06 -7.81 -7.46 0.12 -0.188 -0.191 -0.194 -0.197 EG-W

(a) (b) 0 Figure 3. The Plot of ∆푡푉휙 and ∆푡퐵 vs % (v/v) composition of (a) 1,4-dioxane –water and (b) ethylene glycol-water at T=298.15K respectively.

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0 Table 9. Values of Δt푉휙 and ΔtB of BaBr2 in ethylene glycol- -water and 1,4-dioxane- water at T=(298.15- 313.15) K and 0.1 MPa Pressure. % 1,4-Dioxane-Water Ethylene glycol -Water 5 ퟎ 3 5 ퟎ 5 ퟎ 5 ퟎ (v/v) 10 푽흓/(m 10 Δt푽흓 10 푽흓/ 10 Δt푽흓/ B ΔtB B ΔtB mol-1) /(m3 mol-1) (m3 mol-1) (m3 mol-1) T=298.15K 0 5.312 0.00 0.721 0.00 5.312 0.00 0.721 0.00 10 5.677 0.36 0.743 0.02 5.498 0.19 0.813 0.09 20 5.818 0.51 0.809 0.09 5.720 0.41 0.949 0.23 30 6.145 0.83 0.906 0.18 5.838 0.53 1.066 0.35 T = 303.15K 0 5.221 0.00 0.712 0.00 5.221 0.00 0.712 0.00 10 5.446 0.23 0.730 0.02 5.316 0.09 0.778 0.07 20 5.602 0.38 0.778 0.07 5.460 0.24 0.891 0.18 30 5.908 0.69 0.867 0.16 5.621 0.40 1.004 0.29 T = 308.15K 0 5.103 0.00 0.692 0.00 5.103 0.00 0.692 0.00 10 4.876 -0.23 0.700 0.01 5.168 0.06 0.710 0.02 20 5.133 0.03 0.755 0.06 5.308 0.21 0.811 0.12 30 5.671 0.57 0.851 0.16 5.462 0.36 0.964 0.27 T =313.15K 0 5.001 0.00 0.674 0.00 5.001 0.00 0.674 0.00 10 4.703 -0.30 0.681 0.01 5.013 0.01 0.663 -0.01 20 4.954 -0.05 0.726 0.05 5.143 0.14 0.723 0.05 30 5.465 0.46 0.820 0.15 5.288 0.29 0.919 0.25

4. Conclusions

The results obtained in the above discussions represent that the densities increase when the concentration of BaBr2 and temperature increase. It has been observed that the density of the solutions increases with an increase in the mass fraction of DO and EG. The positive values of B coefficient at all temperatures represent the structure promoting the nature of the solute. The negative value of dB/dT may be attributed to the solid interactions between ions and 0 solvents at the lower temperature. The positive values of 푉ϕ may be due to the existence of 0 strong ion-solvent interactions. The negative values of 퐸훷 and the positive values of Hepler’s constant say that the solute is a structure promoter. The negative values of isobaric thermal 0 expansion, 훼1 and the positive values of (휕퐶푝 ⁄휕푃) support the results obtained from the volumetric and viscometric studies.

Funding

This research received no external funding.

Acknowledgments

One of the authors (BBN) thankful to the Principal of Vikram Deb Autonomous College, Jeypore for providing the laboratory facility.

Conflicts of Interest

The authors declare no conflict of interest.

References

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